Question

Solve the inequality and graph the solution.
s
3
≥3
Plot the endpoints. Select an endpoint to change it from closed to open. Select the middle of the segment, ray, or line to delete it.

Answer 1

To solve the inequality \( s^3 \geq 3 \), we start by isolating \( s \).

1. **Take the cube root of both sides**:
\[
s \geq \sqrt[3]{3}
\]

Since the cube root function is increasing, there are no sign changes needed when taking the cube root.

2. **Identify the solution**:
The solution to the inequality is \( s \) such that:
\[
s \geq \sqrt[3]{3}
\]

3. **Graph the solution**:
- The endpoint \( s = \sqrt[3]{3} \) is included in the solution, so we will use a closed dot.
- The solution extends to positive infinity.
- We represent this graphically as a line starting at \( \sqrt[3]{3} \) (closed dot) and extending to the right.

Here’s a description of the graphing actions:
- Plot \( \sqrt[3]{3} \) on the number line with a closed endpoint (●).
- Draw a line extending to the right of this point indicating all values greater than \( \sqrt[3]{3} \).

If you want to change the endpoint from closed to open for any reason, you could consider what happens if the inequality were strict (\( s^3 > 3 \)), but since here we are working with \( s^3 \geq 3 \), we keep it closed as stated above.

Thus, the final solution can be represented on a number line as follows:

\[
\text{Graph:}
\]
```plaintext
<---|--------|--------|--------|--------|--------|--------|--------|--->
-2 -1 0 1 2 sqrt[3]{3} 3 4
●====================>
```

Here, the filled dot at \( \sqrt[3]{3} \) indicates that \( \sqrt[3]{3} \) is included in the solution, and the right-pointing arrow indicates that the solution goes to positive infinity.